Compound Inequalities

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What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

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How do you solve a compound inequality of the form a ≤ x ≤ b?

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To solve a compound inequality of the form a ≤ x ≤ b, you find the values of x that satisfy both inequalities simultaneously.

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What does the symbol '≤' represent in inequalities?

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The symbol '≤' means 'less than or equal to'.

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What does the symbol '≥' represent in inequalities?

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The symbol '≥' means 'greater than or equal to'.

Front

How do you graph a compound inequality that uses 'and'?

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To graph a compound inequality that uses 'and', you find the intersection of the two inequalities on a number line.

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How do you graph a compound inequality that uses 'or'?

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To graph a compound inequality that uses 'or', you find the union of the two inequalities on a number line.

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What is the solution to the compound inequality -3 ≤ 2x - 1 ≤ 5?

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The solution is -1 ≤ x ≤ 3.

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What is the solution to the compound inequality -2 < x - 9 < 3?

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The solution is 7 < x < 12.

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What does it mean if a compound inequality has no solution?

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It means that there are no values of the variable that satisfy all parts of the inequality.

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What is the difference between 'and' and 'or' in compound inequalities?

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'And' requires both conditions to be true simultaneously, while 'or' allows for either condition to be true.